To answer your first question: you will have to prove your relationship. Marriage is the best way to do this, but you should write a letter about your relationship, get testimonials from your friends and family about the seriousness of your relationship and submit pictures…lots of pictures. This article has some information on the kind of things you should submit.
As to your second question: no, you do not need an LMIA (the new name for LMO) to apply for that work permit. Learn more.